*How do the graph of sine and cosine relate to each of the other? Emphasize asymptotes in your response.*

*1.) Tangent?***Based on the Ratio Identity, tangent equals sine/cosine. Whenever the denominator equal to 0, which means there is an asymptote. So, because cosine is the denominator, it must equal to 0, to have an asymptote.**

As seen in the picture below, the the tangent graph are plotted and have asymptotes. Based on the y-values are 0 for -3pi/2, -pi, pi/2, pi. etc.

*2.) Cotangent?*Based on the Ratio Identity, cotangent is equal to cosine/sine. So that means when sine equal to 0, there will be an asymptote. On the graph below the points that have a value of 0 are -2pi, pi, 0, pi, and 2pi.

*3.) Secant?*Based on the Reciprocal Identity, secant is 1/cos. The graph below shows the asymptote for secant. Which are -pi/2, pi/2, pi, 3pi/2, and 5pi/2.

*4.) Cosecant?*Based on the Reciprocal Identity, cosecant is equal to 1/sin. On the graph below shows the asymptote for cosecant. Which is at pi, and 2pi.

References:

1.) http://www.purplemath.com/modules/triggrph3.htm

2.) http://www.mathsisfun.com/algebra/trig-sin-cos-tan-graphs.html

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